Note: I am using 2*x+cos(x) as an example below. I’m asking this question for any function where Solve[] doesn’t yield a closed form result. My specific interest at the moment is getting Mathematica to spit out the (well known) power series expansion solution of Kepler’s Equation of the Center, just as a test.

The function 2*x+cos(x) is monotonic increasing (derivative is 2-sin(x)), and thus invertible. There’s no simple form for the inverse:

  Solve[2*x+Cos[x] == y, x]                                                    Solve::nsmet: This system cannot be solved with the methods available to Solve.  

Question: can I get a power series approximation to the solution? Either using Mathematica builtin functions or some sort of voodoo?